Electrochemistry

Electrochemistry is about the two-way traffic between chemical energy and electrical energy. A redox reaction that happens spontaneously can be made to push electrons round a wire — that is a cell, and it is how a torch, a mobile phone and an electric vehicle are powered. Run in reverse, electricity forces an unwilling reaction to go — that is electrolysis, and it is how aluminium, chlorine and electroplated metal are made.

5.1 Electrode potential and standard electrode potential

Dip a strip of zinc into water. A few Zn atoms leave the metal as Zn²⁺ ions, leaving their electrons behind:

Zn(s) ⇌ Zn²⁺(aq) + 2e⁻

The metal becomes slightly negative and the layer of solution touching it slightly positive. This electrical double layer stops the process almost at once, and an equilibrium potential difference is set up across the metal–solution boundary.

A metal that loses electrons readily, such as zinc, builds up a negative charge and has a positive oxidation potential. A metal that prefers to take electrons back, such as copper, behaves the other way round. By international convention we always tabulate reduction potentials, and

The value depends on concentration, temperature and gas pressure, so a reference set of conditions is fixed.

5.2 Types of electrodes: standard hydrogen electrode and calomel electrode

Standard hydrogen electrode (SHE). A strip of platinum foil coated with finely divided platinum black is dipped in a 1 M solution of H⁺ ions, and pure hydrogen gas at 1 bar is bubbled over it at 298 K. The platinum takes no part in the reaction; it only provides a surface for the electron transfer and a path for the current. Its half-reaction is

2H⁺(aq) + 2e⁻ ⇌ H₂(g), E° = 0.000 V (by definition)

It is the primary reference electrode, but it is awkward: it needs a supply of very pure hydrogen at constant pressure, the solution must be exactly 1 M, and the platinum surface is poisoned by traces of arsenic or sulphide.

Calomel electrode. For daily laboratory work a secondary reference electrode is used instead. The calomel electrode consists of mercury covered with a paste of mercury(I) chloride, Hg₂Cl₂ (calomel), in contact with a potassium chloride solution, with a platinum wire dipping into the mercury:

Hg(l) | Hg₂Cl₂(s) | KCl(aq)

Hg₂Cl₂(s) + 2e⁻ ⇌ 2Hg(l) + 2Cl⁻(aq)

Its potential depends only on the chloride concentration, which is easy to fix:

KCl solution	Electrode potential
Saturated	+0.242 V
1.0 M	+0.280 V
0.1 M	+0.334 V

It is compact, robust, and keeps a steady potential, so it is the reference half of almost every pH meter.

5.3 Electrochemical series and its applications

Arranging the standard reduction potentials of all electrodes in increasing order gives the electrochemical series (also called the activity series or the electromotive series).

Applications of the electrochemical series

1. Relative strength of reducing agents. The more negative E^{\circ}, the greater the tendency to lose electrons. Li is the strongest reducing agent in the list; Au is the weakest.
2. Relative strength of oxidising agents. The more positive E^{\circ}, the greater the tendency to gain electrons. F₂ is the strongest oxidising agent known in aqueous solution.
3. Predicting displacement reactions. A metal displaces from solution any metal lying below it. Zn (−0.76) displaces Cu (+0.34): Zn + CuSO₄ → ZnSO₄ + Cu. Copper cannot displace zinc.
4. Liberation of hydrogen from acids. Metals above hydrogen (Zn, Fe, Mg, Al) dissolve in dilute HCl or H₂SO₄ giving H₂; Cu, Ag, Hg and Au do not.
5. Calculating the EMF of a cell and deciding which electrode is the anode.
6. Predicting the feasibility of a redox reaction: if the calculated E^{\circ}_{cell} is positive the reaction goes as written.
7. Products of electrolysis. When two cations compete at the cathode, the one with the higher reduction potential is discharged first.
8. Corrosion and its prevention. Iron is protected by coating with a more easily oxidised metal (zinc — galvanising), which corrodes sacrificially.

5.4 Voltaic cell: Zn-Cu cell, Ag-Cu cell

If zinc is dropped into copper sulphate solution, the reaction Zn + Cu²⁺ → Zn²⁺ + Cu occurs at once, but the electrons pass directly from Zn to Cu²⁺ and all the energy appears as heat. A voltaic (galvanic) cell separates the two half-reactions so the electrons are forced to travel through an external wire, where they can do useful work.

The Daniell cell (Zn–Cu cell). A zinc rod stands in 1 M ZnSO₄ in one beaker and a copper rod in 1 M CuSO₄ in another. The rods are joined by a wire through a voltmeter, and the two solutions by a salt bridge — an inverted U-tube packed with a saturated solution of KCl (or KNO₃) set in agar jelly.

Electrode	Name	Sign	Process	Half-reaction
Zn	Anode	−	Oxidation	Zn(s) → Zn²⁺(aq) + 2e⁻
Cu	Cathode	+	Reduction	Cu²⁺(aq) + 2e⁻ → Cu(s)

Overall: Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s), E^{\circ}_{cell} = 1.10 V

The cell is written, by IUPAC convention, with the anode on the left, a single bar for a phase boundary and a double bar for the salt bridge:

Zn(s) | Zn²⁺(1 M) || Cu²⁺(1 M) | Cu(s)

The Ag–Cu cell. Here copper is the more easily oxidised metal, so copper is now the anode and silver the cathode:

Cu(s) | Cu²⁺(1 M) || Ag⁺(1 M) | Ag(s)

Electrode	Half-reaction	E^{\circ} / V
Anode (Cu)	Cu(s) → Cu²⁺(aq) + 2e⁻	-0.34 (oxidation)
Cathode (Ag)	2Ag⁺(aq) + 2e⁻ → 2Ag(s)	+0.80 (reduction)

Overall: Cu(s) + 2Ag⁺(aq) → Cu²⁺(aq) + 2Ag(s), E^{\circ}_{cell} = 0.46 V

Electrolytic cells — the reverse process. If an external source pushes current the other way, a non-spontaneous reaction can be driven. That is an electrolytic cell.

	Galvanic (voltaic) cell	Electrolytic cell
Energy change	Chemical → electrical	Electrical → chemical
Reaction	Spontaneous, \Delta G < 0	Non-spontaneous, \Delta G > 0
Anode	Negative, oxidation	Positive, oxidation
Cathode	Positive, reduction	Negative, reduction
Electrolytes	Two, joined by a salt bridge	One, both electrodes in it
Example	Daniell cell, dry cell	Electroplating, extraction of Na, Al

Note that oxidation always happens at the anode and reduction always at the cathode. Only the signs swap.

5.5 Cell potential and standard cell potential

A positive E^{\circ}_{cell} means the reaction as written is spontaneous. If the answer comes out negative, the cell has been written backwards.

When the concentrations are not 1 M the EMF changes, and the Nernst equation gives the correction. For a general cell reaction aA + bB \rightarrow cC + dD involving n electrons,

The constant follows from 2.303RT/F = 2.303 \times 8.314 \times 298 / 96500 = 0.0591 V. Pure solids and pure liquids do not appear in Q.

5.6 Relationship between cell potential and free energy

The electrical work a cell can deliver is (charge transferred) × (potential difference). For n moles of electrons the charge is nF, where F = 96500 C mol⁻¹ is the Faraday constant — the charge on one mole of electrons, F = N_A e = (6.022\times10^{23})(1.602\times10^{-19}) C.

So a spontaneous cell reaction (\Delta G < 0) is exactly one with a positive EMF, and a large EMF means a large equilibrium constant.

Faraday's laws of electrolysis

The same constant F governs how much substance an electric current deposits.

5.7 Commercial batteries and fuel cells (hydrogen/oxygen)

A battery is one or more galvanic cells packaged for use. Primary cells cannot be recharged because the electrode reaction is not reversible; secondary cells (accumulators) can.

Battery	Anode	Cathode	Electrolyte	EMF	Type
Dry (Leclanché) cell	Zn can	graphite rod in MnO₂ + C	NH₄Cl + ZnCl₂ paste	≈1.5 V	Primary
Lead storage battery	Pb	PbO₂	38 % H₂SO₄	2.0 V per cell	Secondary
Nickel–cadmium cell	Cd	NiO(OH)	KOH	≈1.2 V	Secondary
Lithium-ion cell	graphite holding Li	LiCoO₂	Li salt in organic solvent	≈3.7 V	Secondary

Dry cell. Anode: Zn(s) → Zn²⁺(aq) + 2e⁻. Cathode: 2MnO₂(s) + 2NH₄⁺(aq) + 2e⁻ → Mn₂O₃(s) + 2NH₃(aq) + H₂O(l). It runs down because the zinc case is eaten away and NH₃ collects round the cathode.

Lead storage battery. Used in every car and in inverter backup systems during load-shedding. On discharge:

• Anode: Pb(s) + SO₄²⁻(aq) → PbSO₄(s) + 2e⁻
• Cathode: PbO₂(s) + SO₄²⁻(aq) + 4H⁺(aq) + 2e⁻ → PbSO₄(s) + 2H₂O(l)
• Overall: Pb + PbO₂ + 2H₂SO₄ → 2PbSO₄ + 2H₂O

On charging the whole reaction is reversed, regenerating Pb and PbO₂ and restoring the acid. Because sulphuric acid is consumed on discharge, the state of charge can be checked by measuring the density of the acid with a hydrometer.

Fuel cells. A fuel cell is a galvanic cell in which the reactants are supplied continuously from outside, so the cell never "runs down". The hydrogen–oxygen fuel cell used on the Apollo spacecraft is the standard example.

• Anode: 2H₂(g) + 4OH⁻(aq) → 4H₂O(l) + 4e⁻
• Cathode: O₂(g) + 2H₂O(l) + 4e⁻ → 4OH⁻(aq)
• Overall: 2H₂(g) + O₂(g) → 2H₂O(l), E^{\circ}_{cell} = 1.23 V

Advantages: efficiency of 70–75 % against about 40 % for a thermal power station, because the energy is not first turned into heat; no smoke, no oxides of nitrogen or sulphur, and the only product is drinkable water; it runs continuously as long as fuel is supplied. Disadvantages: the platinum catalyst is expensive, and hydrogen is difficult to store and transport safely.

Chapter summary

• Electrode potential arises from the electrical double layer at a metal–solution boundary; only differences can be measured, so all E^{\circ} values are quoted against the SHE (1 M H⁺, H₂ at 1 bar, 298 K, defined as 0.000 V). The calomel electrode (+0.242 V saturated) is the practical secondary reference.
• The electrochemical series orders standard reduction potentials. More negative = better reducing agent; more positive = better oxidising agent. A metal displaces any metal below it, and metals above hydrogen liberate H₂ from dilute acids.
• In a galvanic cell, oxidation occurs at the negative anode (written on the left) and reduction at the positive cathode. Daniell cell: Zn | Zn²⁺(1 M) || Cu²⁺(1 M) | Cu, E^{\circ}_{cell} = 1.10 V. Ag–Cu cell: Cu | Cu²⁺ || Ag⁺ | Ag, E^{\circ}_{cell} = 0.46 V.
• E^{\circ}_{cell} = E^{\circ}_{cathode} - E^{\circ}_{anode}; positive means spontaneous. E^{\circ} is intensive and is never multiplied by a stoichiometric coefficient.
• Nernst equation: E_{cell} = E^{\circ}_{cell} - \frac{0.0591}{n}\log Q at 298 K.
• \Delta G = -nFE_{cell}, \Delta G^{\circ} = -nFE^{\circ}_{cell} and \log K = nE^{\circ}_{cell}/0.0591, with F = 96500 C mol⁻¹.
• Faraday: Q = it; 96500 C liberates one gram-equivalent of any substance.
• Primary cells (dry cell) cannot be recharged; secondary cells (lead storage, Ni–Cd, Li-ion) can. The H₂–O₂ fuel cell is fed continuously, E^{\circ}_{cell} = 1.23 V, and produces only water.

Practice questions

Group A — Multiple choice (1 mark each)

1. The standard electrode potential of the standard hydrogen electrode at 298 K is [1]a0.00 Vb0.242 Vc1.00 Vd−0.76 V
2. In a galvanic cell the anode is [1]apositive and reduction occursbnegative and oxidation occurscnegative and reduction occursdpositive and oxidation occurs
3. Which of these metals cannot liberate hydrogen from dilute hydrochloric acid? [1]aZnbFecMgdCu
4. For the cell Zn | Zn²⁺ || Cu²⁺ | Cu, given E^{\circ} values of −0.76 V and +0.34 V, the standard cell potential is [1]a0.42 Vb1.10 Vc−1.10 Vd0.34 V
5. The quantity of charge carried by one mole of electrons is about [1]a9650 Cb96500 Cc1.6\times10^{-19} Cd6.02\times10^{23} C
6. If E^{\circ}_{cell} is positive, then \Delta G^{\circ} for the cell reaction is [1]apositivebzerocnegativedunpredictable

Answers to Group A

1. (a) — it is the arbitrary zero of the whole scale.

2. (b) — electrons are released there, so it is the negative terminal of a galvanic cell.

3. (d) — copper lies below hydrogen in the electrochemical series.

4. (b) — E^{\circ}_{cell} = 0.34 - (-0.76) = 1.10 V.

5. (b) — one faraday, F = N_Ae \approx 96500 C mol⁻¹.

6. (c) — \Delta G^{\circ} = -nFE^{\circ}_{cell}, and n and F are positive.

Group B — Short answer (5 marks each)

1. Define electrode potential and standard electrode potential. Describe the construction and working of the standard hydrogen electrode with a labelled diagram, and give two of its limitations. [5]
2. What is a salt bridge? Give its three functions. Describe the Daniell cell, writing the electrode reactions, the overall reaction and the cell notation. [5]
3. State any five applications of the electrochemical series. [5]
4. Calculate the EMF at 298 K of the cell Zn(s) | Zn²⁺(0.01 M) || Cu²⁺(0.1 M) | Cu(s), given E^{\circ}_{cell} = 1.10 V. [5]
5. A current of 1.5 A is passed through a silver nitrate solution for 20 minutes. Calculate the mass of silver deposited. (Ag = 108) [5]
6. Explain with electrode reactions the working of the hydrogen–oxygen fuel cell, and state two advantages over a thermal power plant. [5]

Answers to Group B

4. The cell reaction is Zn + Cu²⁺ → Zn²⁺ + Cu with n = 2, so

Q = \frac{[\text{Zn}^{2+}]}{[\text{Cu}^{2+}]} = \frac{0.01}{0.1} = 0.1, \qquad \log Q = -1

E_{cell} = 1.10 - \frac{0.0591}{2}(-1) = 1.10 + 0.0296 = 1.13\ \text{V}

5. Q = it = 1.5 \times 20 \times 60 = 1800 C. Since Ag⁺ + e⁻ → Ag needs one electron per silver atom,

n(\text{Ag}) = \frac{1800}{96500} = 0.01865\ \text{mol}, \qquad m = 0.01865 \times 108 = 2.01\ \text{g}

6. Anode: 2H₂ + 4OH⁻ → 4H₂O + 4e⁻. Cathode: O₂ + 2H₂O + 4e⁻ → 4OH⁻. Overall 2H₂ + O₂ → 2H₂O, E^{\circ}_{cell} = 1.23 V. Advantages: much higher conversion efficiency (about 70 % against 40 %) because no heat engine is involved, and no polluting emissions — the product is pure water.

Group C — Long answer (8 marks each)

1. (a) Derive the relation \Delta G^{\circ} = -nFE^{\circ}_{cell} and hence obtain an expression relating E^{\circ}_{cell} to the equilibrium constant. [4](b) For the cell Cu | Cu²⁺(1 M) || Ag⁺(1 M) | Ag, E^{\circ}_{cell} = 0.46 V. Calculate \Delta G^{\circ} and K at 298 K, and comment on the extent of the reaction. [4]
2. (a) With a labelled diagram, describe the construction, discharge and charging reactions of the lead storage battery. [5](b) Distinguish between a galvanic cell and an electrolytic cell on any three grounds, and state Faraday's two laws of electrolysis. [3]

Answers to Group C

1.(b) The cell reaction Cu + 2Ag⁺ → Cu²⁺ + 2Ag transfers n = 2 electrons.

\Delta G^{\circ} = -nFE^{\circ}_{cell} = -(2)(96500)(0.46) = -88780\ \text{J mol}^{-1} = -88.8\ \text{kJ mol}^{-1}

\log K = \frac{nE^{\circ}_{cell}}{0.0591} = \frac{0.92}{0.0591} = 15.57 \;\Longrightarrow\; K = 3.7\times10^{15}

K is very large, so the reaction goes essentially to completion: copper dissolves and silver is deposited almost quantitatively.

2.(a) Lead plates packed with spongy Pb form the anode, plates packed with PbO₂ the cathode, both dipping in about 38 % H₂SO₄. Discharge: Pb + SO₄²⁻ → PbSO₄ + 2e⁻ at the anode and PbO₂ + SO₄²⁻ + 4H⁺ + 2e⁻ → PbSO₄ + 2H₂O at the cathode, overall Pb + PbO₂ + 2H₂SO₄ → 2PbSO₄ + 2H₂O, giving 2.0 V per cell. Charging drives the same equation backwards: 2PbSO₄ + 2H₂O → Pb + PbO₂ + 2H₂SO₄.

2.(b) Galvanic: spontaneous, converts chemical to electrical energy, anode negative, two electrolytes joined by a salt bridge. Electrolytic: non-spontaneous, converts electrical to chemical energy, anode positive, one electrolyte. Faraday's first law: the mass liberated at an electrode is proportional to the quantity of electricity passed, m = Zit. Second law: with the same quantity of electricity, the masses liberated in different electrolytes are proportional to their equivalent weights.